Researching The Preparation of Specialized Mathematics and Science Upper
Elementary/Middle-Level Teachers: The 2nd Year Report
[Return to MCTP Research Page]
J. Randy McGinnis, Gilli Shama, Amy-Roth McDuffie, Mary Ann Huntley, and
University of Maryland at College Park
Tad Watanabe, Towson State University
Paper presented at the annual meeting of the National Science Teachers Association,
St. Louis, Missouri, March 28-31, 1996
The preparation of this manuscript was supported in part by a grant from
the National Science Foundation.
(NSF Cooperative Agreement No. DUE 9255745)
Researching The Preparation of Specialized Mathematics and Science Upper
Elementary/Middle-Level Teachers: The 2nd Year Report
The Maryland Collaborative for Teacher Preparation (MCTP) is a National
Science Foundation funded statewide undergraduate program for students who
plan to become specialist mathematics and science upper elementary or middle
level teachers. The goal of the MCTP is to promote the development of teachers
who are confident teaching mathematics and science, and who can provide
an exciting and challenging learning environment for students of diverse
The purpose of this report is to orient the reader to the Maryland Collaborative
for Teacher Preparation and to give an overview of the on-going research
activities being conducted within the project. Structurally, the paper is
divided into two sections: Section One contains an overview of the Maryland
Collaborative for Teacher Preparation and the Research Group, Section Two
contains summaries of four research studies conducted within the Reseach
Interested readers who desire additional information are encouraged to conduct
the MCTP Co-Directors of Research: J. Randy McGinnis, email@example.com,
(301) 405-6234 and Tad Watanabe, Tad@midget.towson.edu, (410) 830-3585.
Section One: Overview of the Maryland Collaborative for Teacher Preparation
and the Research Group
The MCTP consists of the following:
* Specially designed courses in science and mathematics, taught by instructors
committed to a hands-on, minds-on interdisciplinary approach.
* Internship experiences with research opportunities in business, industrial
and scientific settings, and with teaching activities in science centers,
zoos, and other institutions.
* Field experiences and student teaching situations with mentors devoted
to the interdisciplinary approach to mathematics and science.
* Modern technologies as standard tools for planning and assessment, classroom
and laboratory work, problem-solving and research
* Placement assistance and sustained support during the induction year in
the teaching profession
* Financial support for qualified students.
History of the MCTP
The National Science Foundation selected Maryland in 1993 as one
of the first three states awarded Collaborative Teacher Preparation Grants
(spread out over a five-year period) to develop and implement an interdisciplinary
program for intending elementary and middle school teachers to become science/mathematics
specialists. Higher education institutions involved in this grant include
a number of University of Maryland institutions. Public school districts
involved include Baltimore County and Prince George's County. The project
management team consists of Jim Fey, Project Director, Co-Principal DirectorsGenevieve
Knight, Tom O'Haver, and John Layman, and Executive Director Susan Boyer.
Various committees working on the MCTP include the Content Teaching Committee,
the Pedagogical Committee, and the Research Group. These committees are
charged with developing and researching new college-level content and methods
courses for recruited teacher candidates who started in the program in the
fall of 1994.
What is the history and leadership of the Research Group?
In late July 1994, Fey, MCTP Project Director, asked J. Randy McGinnis (Science
Educator), University of Maryland at College Park (UMCP), andTad Watanabe
(Mathematics Educator), Towson State University (TSU), to share the leadership
of a Research Component of the MCTP. Anna Graeber, University of Maryland
at College Park, and Co-Director of the MCTP Methods Group, agreed to act
as a mentor to the Research Group. Amy Roth-McDuffie, Mary Ann Huntley,
Karen King andSteve Kramer, doctoral mathematics education students at UMCP,
have served as graduate research assistants to the Research Group. Gilli
Shama, a visiting Israeli mathematics educator, also joined the Research
Group in the fall, 1995.
Who constitutes the Research Group?
The leadership of the Research Group identified and recruited Institutional
Research Representatives (IRR) who would coordinate research efforts at
the participating institutions offering MCTP courses. The individuals who
took on this responsibility are Dr. Renny Azzi, Frostburg State University,
Dr. Delores Harvey, Coppin State College, Dr. Joan Langdon, Bowie State
University, and Dr. Gerry Rossi, Salisbury State University. Dr. Randy McGinnis
and Dr. Tad Watanabe also took on this responsibility for their institutions,
What is the purpose of MCTP research?
In essence, the primary purpose of research in the MCTP is directed
at knowledge growth in undergraduate mathematics and science teacher education.
The unique elements of the MCTP (particularly the instruction of mathematical
and scientific concepts and reasoning methods in undergraduate content and
methods courses that model the practice of active, interdisciplinary teaching)
are being longitudinally documented and interpreted from two foci: the faculty
and the teacher candidate perspectives.
What are the guiding research questions addressed in the MCTP research?
The following questions serve as the a priori research questions
(a posteriori questions will emerge throughout the research period):
1. What is the nature of the faculty and teacher candidates' beliefs and
attitudes concerning the nature of mathematics and science, the interdisciplinary
teaching and learning of mathematics and science to diverse groups (both
on the higher education and upper elementary and middle level), and the
use of technology in teaching and learning mathematics and science?
2. Do the faculty and teacher candidates perceive the instruction in the
MCTP as responsive to prior knowledge, addressing conceptual change, establishing
connections among disciplines, incorporating technology, promoting reflection
on changes in thinking, stressing logic and fundamental principles as opposed
to memorization of unconnected facts, and modeling the kind of teaching/learning
they would like to see on the upper elementary, middle level?
Answers to those questions will address the following global research questions
driving teacher education research:
1. How do teacher candidates construct the various facets of their knowledge
2. What nature of teacher knowledge is requisite for effective teaching
in a variety of contexts?
3. What specific analogies, metaphors, pitfalls, examples, demonstrations,
and anecdotes should be taught content/method professors so that teacher
candidates have some knowledge to associate with specific content topics?
What data are being collected for MCTP research?
Both numerical and qualitative data are being collected to address
the MCTP research questions. Numerical data derive from the administration
of two Likkert-type surveys developed by the MCTP Research Group: a college
student version and a faculty version of "Attitudes and Beliefs About
The Nature Of And The Teaching Of Mathematics And Science". Participating
faculty and students in MCTP classes (both MCTP teacher candidates and non-MCTP
students) contribute to this data base. Data are analyzed using the software
Qualitative data derive from semi-structured ongoing interviews with participants
in MCTP classes, MCTP class observations, participant journals, and MCTP
course materials. Standard qualitative analysis techniques (analytic induction,
constant comparison, and discourse analysis) assist in the interpretation
and presentation of case studies emerging from this rich data set. The software
program NUD.IST. facilitates the data analysis.
Section Two: Summary of Four On-Going Research Studies in the Maryland
Collaborative for Teacher Preparation
This section contains summaries of four studies conducted within the Maryland
Collaboration for Teacher Preparation. Study One focuses on a statistical
examination of data from the college student version of the MCTP "Attitudes
and Beliefs About The Nature Of And The Teaching Of Mathematics And Science"
instrument. Study Two focuses on a discourse examination of the mathematics
and science MCTP faculty discussing science and mathematics. Study Three
focuses on the perception of MCTP teaching faculty on the integration of
mathematics and science and on barriers to implementing integration in their
classes. And Study Four focuses on the teaching practices of a MCTP mathematics
Study One: Statistical Examination Of College Students' Responses On
The MCTP College Student Survey
During the summer of 1994, the MCTP Research Group developed a Likkert-type
instrument to determine the beliefs and attitudes college level students
held in MCTP classes. A pilot version of the survey was administered, during
the 1994-1995 school year, to hundreds of students enrolled in MCTP classes
throughout the state participating in the project. During the summer of
1995, the survey was revised to address concerns made apparent during the
pilot administrations. These concerns included wording of some items, placement
of demographic data and more explicit directions. Appendix A contains a
copy of the revised 48-item college student survey, "Attitudes and
Beliefs about the Nature of and the Teaching of Mathematics and Science."
During the beginning of the fall 1995 semester the survey was administrated
to 807 students enrolled in twenty-one mathematics, biology and physics
MCTP classes, offered at 7 institutions of higher learning in Maryland,
and two large lecture biology classes offered at another institution. Of
that sample, 57 were dropped due to various irregularities in instrument
administration. The responses from the remaining 750 served for examining
the instrument's validity and reliability. Factor analysis was performed
on the 32 general items, and separately on 9 items that were for intending
teachers only (7 items were on demographics). A pre-designed structure of
five subscales was supported. The five subscales, and there estimated reliability
by Cronbach's alpha, are:
(a) Beliefs about the nature of mathematics and science (alpha=0.745);
(b) Beliefs about the teaching of mathematics and science (alpha=0.681);
(c) Attitudes toward mathematics and science (alpha=0.801);
(d) Attitudes toward learning to teach mathematics and science (alpha=0.807);
(e) Attitudes toward the teaching of mathematics and science (alpha=0.596).
The estimation of the instrument's reliability is the median of subscales
The survey was administrated to all 21 MCTP classes once at the beginning
of the fall 1995 semester (pre-test), and once at the end of the same semester
(post-test). The responses of the students in the large lecture hall biology
class were removed from further analysis since the context of their learning
environment was so different from the other small classes. The remaining
391 students who contributed the pre-test were analyzed. Of those respondents,
97 identified themselves as MCTP students, and 216 as non-MCTP pre-service
teachers. The responses of 375 students to the post-test were analyzed.
Of those respondents, 83 identified themselves as MCTP students, and 176
as non-MCTP prospective teachers.
Summary of Emergent Understandings
Data analysis of the survey results included a comparison of pre-test results
to post-test results, and a comparison of responses between MCTP candidates
and non-MCTP candidates. Significance of means differences was examined
General results indicate that the sample population's pre-test means on
the subscales (on a range of 1 to 5, where 5 is positive) were 3.81, 2.97,
2.39, 3.16, and 2.18 respectively. The sample population's post-test means
on the subscales were 3.71, 3.05, 2.41, 3.03, and 2.18
respectively. On the positive side, all students' mean on beliefs about
the teaching of mathematics and science have significantly increased. This
increase was due to an increase in students' mean over items relating to
beliefs about the use of technology for teaching mathematics and science.
The most unanticipated significant finding from a comparison of the pre-test
and post-test results was the significant decline in the students mean in
the beliefs about the nature of mathematics and science subscale.
A comparison of pre-test results between the 97 MCTP candidates and the
remaining 216 intending teachers students was conducted. It was found that,
on each of the subscales, the MCTP candidates' mean was significantly higher
then other students' mean. However, the comparsion of post-test results
paint a different story. We could not reject the assumptions that MCTP candidates'
post-test means are equal to the other intending teachers' mean on the subscale
of beliefs about the nature of mathematics and science, on the subscale
of beliefs about the teaching of mathematics and science, and on the subscale
of attitudes toward the teaching of mathematics and science. In comparing
the MCTP candidates' pre-and post-test means on the subscale of attitudes
toward the teaching of mathematics and science, it was also found that they
have significantly declined from pre-test to post-test.
These findings are from one semester. Future semesters will also be analyzed
for changes since this is a longitudinal study. Of particular interest is
documentation of changes of MCTP teacher candidates over their entire undergraduate
programs of study.
Study Two: University Science and Mathematics Content Professors Talk
The Others' Discipline: An Examination of the Role of Discourse Among Professors
Involved in A Collaborative Mathematics/Science
The notion of 'collaboration' has become an important idea in the field
of education. A number of recent studies have investigated the classroom
culture with an underlying assumption that learning/teaching is a collaborative
effort involving teachers and students (e.g., Cobb, Wood, Yackel, &
McNeal, 1992). This development is consistent with the basic premises of
the social constructivist perspective of learning/teaching, which has become
Because teacher development is also a process of learning/teaching, and
because being a teacher involves a wide range of knowledge (Shulman, 1987),
'collaboration' is crucial. A number of recent reform documents (e.g., AAAS,
1994; NCTM, 1991) call for collaborations among universities/colleges/community
colleges, K-12 schools, business, and government agencies in preparing future
teachers. Since 1993, the National Science Foundation has awarded several
highly funded grants to the projects which aim to reform teacher education
programs under the program, Collaborative for Excellence in Teacher Preparation.
Summary or Emerging Understandings
In this research study focus, a discourse analysis is performed on conversations
among inter-institutions university mathematicians and scientists participating
in reforming content classes for teacher candidates in the Maryland Collaborative
for Teacher Preparation (MCTP). Discourse as used in this study is defined
as the dynamic interplay of dialogue between individuals that includes the
use of rules developed by certain groups of people (Gee, 1990). The focus
on discourse in this study is the result of recent theoretical views that
stress the importance of the environment in which members of a community
communicate (Greeno, 1991; Rogoff, 1990). Conversations or `talk' is recognized
as a particularly revealing resource in analyzing social interactions for
patterns that can promote sense making of a community (Lemke, 1990; McCarthy,
1994). Talking is a communicative event in which the conversants collaborate
in constructing a social text and an academic text simultaneously (Green,
Weade, & Graham, 1988). The social text is the agreed upon rules and
purposes for the social interactions. The academic text is the content of
In this study, content expertise and an interest in reforming content classes
for teacher candidates defined membership in either the science teacher
preparation speech community or the mathematics teacher preparation speech
community. Sharing ideas on the integration of mathematics and science in
MCTP undergraduate content classes served as the purpose of the social text.
The content of the discussion varied in the two speech communities but one
consensus theme emerged: a recognized need to go beyond the connections
of each content and to gain insight into the nature of the `others' discipline
expertise by direct collaboration with an expert in the others content.
"The new vision of the teaching of science and mathematics "(mathematician,
conversation 6/10/95) required this. The experience of searching for this
assistance among the usual members of the content speech community proved
to be deficient in supplying the depth of understanding of the others' content
which they felt should distinguish a truly integrated mathematics/science
content class. Spurred on by this realization as a result of a newly formed
inter-institutional dialogue, pioneers in the separate speech communities
boldly made plans to create an intra-institutional dialogue with other pioneers
from the other content speech community. A critical implication of this
study is the role of dialogue in both inter- and intra-institutional to
promote collaboration between mathematics and science content professors
involved in teacher preparation.
American Association for the Advancement of Science (1993). Benchmarks
for Science Literacy. New York: Oxford University Press.
Bickel, W.E., & Hattrup, R.A. (1995). Teachers and researchers in collaboration:
Reflections on the process. American Educational Research Journal,
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics
mathematics traditions: An interactional analysis. American Educational
Research Journal, 29, 573- 604.
Denton, J.J., & Metcalf, T. (1993). Two school-university collaborations:
Characteristics and findings from classroom observations. (Report No. EA
025227) Atlanta, GA: Paper presented at the annual meeting of the American
Educational Research Association. (ERIC Document Reproduction Service No.
Gee, J. (1990). Social linguistics and literacies: Ideology in discourses.
Green, J.L., Weade, R.,& Graham, K. (1988). Lesson construction and
student participation: A sociolinguistic analysis. In J.L. Green & J.O.
Harker (eds.), Multiple perspective analyses of classroom discourse
(pp. 11-47). Norwood, NJ: Ablex.
Greeno, J.G. (1991). Number sense as situated knowing in a conceptual domain.
Journal in Research in Mathematics Education, 22, 170-218.
Lemke, J. (1990). Talking science: Language, learning and values.
Norwood, NJ: Ablex.
McCarthy, S.J. (1994). Authors, text, and talk: The internalization of dialogue
from social interaction during writing. Reading Research Quarterly,
National Council of Teachers of Mathematics (1991). Professional standards
for teaching mathematics. Reston, Virginia: Author.
Ross, J., Armstrong, R., Nicol, S. & Theilman, L. (1994). The making
of the faculty: Fostering professional development through a collaborative
science community. (Report No. SE 054585). Paper presented at the annual
meeting of the American Association for Higher Education. (ERIC Document
Reproduction Service No. ED 370812).
Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development
in social context. New York: Oxford University Press.
Shulman, L.S. (1987). Knowledge and teaching: Foundations of new reform.
Harvard Educational Review, 57, 1-22.
Study Three: Integrating Mathematics and Science in Undergraduate Teacher
Education Programs: Faculty Voices from Maryland Collaborative for Teacher
The focus of this study is on investigating how university/college instructors
who were teaching MCTP mathematics and science courses during the 1994-1995
school year perceived the nature of these disciplines as well as the connections
between them. The two primary sources of the data for this analysis were
semi-structured interviews with individual instructors conducted during
the 1994 - 95 school year and two content area debriefing meetings held
during the summer of 1995.
Specifically, the following three questions addressed in this study include:
* What are the perceptions of MCTP faculty about the "other" discipline?
* What are the perceptions of MCTP faculty about the connections between
mathematics and science?
* What are some barriers in implementing mathematics and science courses
that emphasize connections?
The instructors of MCTP courses were interviewed twice during the semester
in which they were teaching MCTP courses. In addition, instructors who were
not teaching an MCTP course during the second semester were interviewed
once during that semester.
The interviews were semi-structured in that there was a set of standard
questions that were asked of all participants (see Appendix B). Additional
questions were posed reflecting the responses of the participants. To answer
the specific questions listed above, we have focused primarily on the participants'
responses to the first question in both interview protocols. However, their
responses to other questions, for example question 13 in interview 2, also
related to the research questions, and participants' responses to other
questions were also included as appropriate.
Altogether, forty interviews involving 16 mathematics and science instructors
from four institutions were conducted. There were four mathematics instructors
attending the mathematics debriefing meeting, while nine science instructors
attended the science debriefing meeting. All interviews and group meetings
were audio- and/or video-recorded and transcribed for subsequent analysis.
Summary of Emerging Understandings
It appears that the MCTP university/college faculty members have developed
a renewed sense of respect and appreciation for each other and each other's
discipline. At the same time, they are still struggling with a number of
issues. One such issue that is of particular interest to mathematics educators
is the nature of mathematics in relationship to science. On the one hand,
there is a tendency/desire on the part of mathematics instructors to treat
mathematics as a distinct and independent discipline of its own right. This
perspective reflected the concern on the part of mathematicians and mathematics
educators that science instructors would simply treat mathematics as a tool
and "the nature of what mathematics is is very often not explored in
science" (mathematics instructor, June, 1995). On the other hand, there
is also a perspective that mathematics is a science:
We've always said that mathematics was the queen of all sciences, and some
of us even say that we want to talk about the mathematical sciences. So,
I think we ourselves are part of science. (mathematics instructor, June,
Thus, it appears that participation in the MCTP project has raised a fundamental
question among mathematicians and mathematics educators concerning their
own discipline, as well as the nature of the relationship between mathematics
and science. Most, if not all, mathematics instructors agree that mathematics-science
connections are important and useful; however, many appear to be grappling
with the nature of these connections. Is there something special about the
connections between mathematics and science that are not shared by connections
between mathematics and, for example, economics? Tentative findings seem
to imply that the answer to this question is yes. On the other hand, the
recommendations of the NCTM Standards seem to take a broader perspective
of the notion of connections. Thus, the nature of the relationship between
mathematics and science appears to be an open question not just among the
MCTP project participants. As we continue to gather data from these participants,
we hope to be able to document how this issue is considered by these participants.References
Gee, J. (1990). Social linguistics and literacies: Ideology in discourse.
Glaser, B.G. & Strauss, A.L. (1967). The discovery of grounded theory:
Strategies for qualitative research. New York: Aldine Publishing Company.
Lemke, J. (1990). Talking science: Language learning and values.
Norwood, NJ: Ablex.
Lortie, D.C. (1975). Schoolteacher: A sociological study. Chicago:
University of Chicago Press.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation
standards for school mathematics. Reston, VA: The Council.
National Council of Teachers of Mathematics (1991). Professional standards
for teaching mathematics. Reston, VA: The Council.
Rutherford, F.J. & Ahlgren, A. (1990). Science for all Americans.
New York: Oxford University Press.
Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform.
Harvard Educational Review, 57(1), 1-22.
Skemp, R. (1978). Relational understanding and instrumental understanding.
Arithmetic Teacher, 26(3), 9-15.
Study Four: Modeling Reform-Style Teaching in a College Mathematics Class
from the Perspectives of Professor and Students
This study focuses on the perceptions of five pre-service teachers and their
mathematics professor as participants in a reform-style mathematics classroom.
The goal is to promote understanding which can inform future research on
the teaching and learning practices of college level mathematics instructors
from a constructivist perspective and thus contribute to the preparation
of pre-service mathematics teachers.
Mathematics education in the United States is in the midst of reform. The
National Council of Teachers of Mathematics [NCTM] (1989, 1991, 1995), the
Mathematical Sciences Education Board [MSEB] (1990, 1991, 1995), the Mathematical
Association of America [MAA] (Tucker & Leitzel, 1995) and the National
Research Council [NRC](1991) have issued documents proposing a framework
for change in mathematics education at all levels, elementary through college.
The framework is based on the philosophy that students are active learners
who construct knowledge through their interpretations of the world around
them. The above reform documents present goals for mathematics education
which state that all students should: learn to value mathematics, become
confident in their ability to do mathematics, become mathematical problem
solvers, learn to communicate mathematically, and learn to reason mathematically.
The purpose of this qualitative case study was to provide a description
and an interpretation of a MCTP professor and five MCTP students who are
attempting to teach and learn in a class consistent with the goals set forth
by the reform documents. This study addressed the following a priori research
question: Do the instructor and the pre-service teachers perceive the instruction
in their mathematics course as modeling the kind of teaching/learning they
would like to promote as upper elementary/middle level teachers of mathematics
and science? And if so, how?
Several publications directed at college mathematics teachers stress the
importance of modeling reform-style teaching to undergraduate students (MAA,
1988; MSEB, 1995; NRC, 1991; National Science Foundation [NSF], 1993; Tucker
& Leitzel, 1995). Modeling reform-style teaching at the college level
is important for the following reasons. First, since the literature on teacher
education posits that teachers tend to teach as they have been taught when
they were students (Brown & Borko, 1992; Kennedy, 1991), teachers (including
college level teachers) should model the type of teaching that is consistent
with the reform documents, (MSEB, 1995). Second, as a consequence of this
finding, there are implications specific to college teaching. While all
teachers serve as role models for students who want to become teachers,
college faculty are the people teaching pre-service teachers as they train
for their careers; thus, college faculty should be especially concerned
about modeling good teaching. "Unless college and university mathematicians
model through their own teaching effective strategies that engage students
in their own learning, school teachers will continue to present mathematics
as a dry subject to be learned by imitation and memorization" (NRC,
1991, p. 29). Third, the result of modeling good teaching is a better education
for all students, not just future teachers (NRC, 1991; NSF, 1993).
The research was conducted from a perspective which combines ideas of interactionism
and constructivism. This perspective is consistent with the philosophy toward
teaching and learning that underlies the framework for reform in mathematics
education and with the philosophy of the Maryland Collaborative for Teacher
Preparation [MCTP] which is described above. First, according to the perspective
of interactionism, people invent symbols to communicate meaning and interpret
experiences (Alasuutari, 1995; Blumer, 1986); moreover, people create and
sustain social life through interactions and patterns of conduct including
discourse (Alasuutari, 1995; Gee, 1990; Hicks, 1995; Lave & Wenger,
1991). Furthermore, this position is in accordance with the constructivist
perspective of learning in that individuals develop understandings based
on their experiences and knowledge as it is socially constructed (Ernest,
Cobb and Bauersfeld (1995) discuss the social aspects of learning and knowledge
by advocating viewing mathematics education through the perspectives of
interactionism and constructivism. Incorporating the interactionist perspective
with constructivism, Cobb and Bauersfeld (1995) state that,
They draw on von Glasersfeld's (1987) characterization of students as active
creators of their ways of mathematical knowing, and on the interactionist
view that learning involves the interactive constitution of mathematical
meanings in a (classroom) culture. Further, the authors assume that this
culture is brought forth jointly (by teachers and students), and the process
of negotiating meanings mediates between cognition and culture (p. 1).
As part of this case study, the professor and the students engaged in on-going
interviews and observations throughout the semester to obtain data regarding
their perceptions and actions of toward teaching and learning and the extent
to which the instruction modeled the kind of teaching and learning appropriate
for grades 4 through 8. The data were collected and analyzed through the
use of the qualitative techniques of analytic induction, constant comparison,
and discourse analysis for patterns of similarities and differences between
the professor's and students' perceptions (Bogdan & Biklen, 1992; Gee,
1990; Goetz & LeCompte, 1984).
Summary of Emerging Understandings
An analysis of the data indicated that Dr. Taylor and the students perceived
significant differences between "traditional instruction" and
the teaching and learning "this way" as modeled by Dr. Taylor.
Moreover, both Dr. Taylor and the students expressed a clear image of what
they thought teaching in grades 4 through 8 should be. This image of ideal
teaching was quite consistent with the teaching and learning that they experienced
in Dr. Taylor's class. The experiences of these students and this professor
has implications for teacher education programs interested in preparing
pre-service teachers to achieve the standards for teaching and learning
set forth in the reform documents.
A major implication gained from this qualitative study is that the college
students who experienced a reform-style mathematics classroom completed
a first step in achieving the vision for reform of mathematics education:
constructing an initial model of mathematics teaching and learning which
embraces the ideals of the reform movement. However, this initial experience
as a student in a reform-style mathematics classroom is not enough for preparing
pre-service teachers. In accordance with the findings of Borko, Eisenhart,
and colleagues (Borko, et al., 1992; Eisenhart, et al., 1993), the students
in Dr. Taylor's class believed that further educational coursework and field
experiences would be necessary before they would be prepared to "do
the things that [Dr. Taylor is] doing now" (Beth, Interview, 12/8/94)
in their own teaching. This finding suggests that while one content course
taught from a constructivist perspective is not sufficient in preparing
pre-service teachers to meet the goals for reform, it is necessary to begin
the process of preparing pre-service teachers to incorporate reform-based
practices into their future mathematics teaching.
Another implication for the preparation of pre-service teachers rests in
what was not discussed or taught in Dr. Taylor's class. In observing the
classes and talking to the participants, the researcher never heard overt
talk about how the students' experiences in Dr. Taylor's class might translate
to the students' future practice as elementary/middle school teachers unless
they were specifically asked to discuss this by the researcher. It seems
that discussions of pedagogical issues relevant to pre-service teachers
were considered to be inappropriate discourse.
Why is it significant that pedagogy was not discussed in a mathematics course?
Shulman (1986) brought the notion of pedagogical content knowledge to the
forefront of teacher education. He defines pedagogical content knowledge
as going "beyond knowledge of subject matter per se to the dimension
of subject matter knowledge for teaching " (Shulman, 1986, p. 9) Included
in the category of pedagogical content knowledge are: "the ways for
representing and formulating the subject that make it comprehensible to
others, [and] . . . an understanding of what makes the learning of specific
topics easy or difficult" (Shulman, 1986, p. 9). Shulman (1986) calls
for teacher education programs which offer instruction focusing on content
that includes "knowledge of the structures of one's subject, pedagogical
knowledge of the general and specific topics of the domain, and specialized
curricular knowledge" (p. 13). In other words, pre-service teachers
need to learn about the pedagogical issues in the context of subject matter
knowledge. This need is also stated in the reform documents (e.g., NCTM,
The need for pedagogical content knowledge has implications for classes
like Dr. Taylor's. Dr. Taylor seems to have sound reasons for focusing on
content at the near exclusion of pedagogical discussions, and many other
mathematics and mathematics education faculty probably agree with his reasons.
However, does this mean that pedagogical discussions must be delayed until
pre-professional education courses? It seems that to delay would be missing
a significant opportunity for the development of pedagogical content knowledge.
If professors are unwilling or unable to include pedagogical discussions
in mathematics content courses, then perhaps providing opportunities such
as the MCTP seminar (a seminar which focuses on pedagogical issues as they
relate to the students' content courses) is important for pre-service teachers.
In other words, if conversations which promote reflecting on and making
connections between the pre-service teachers' learning experiences in a
mathematics course and their future teaching are not taking place in mathematics
classrooms, then teacher education programs should consider initiating forums
where this type of conversation can take place in order to enhance pedagogical
content knowledge.Selected References
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We would like to acknowledge the technical contributions of Karen King and
Gilli Shama, SPSS data analysis, and Steve Kramer, NUD.IST data analysis.
APPENDIX A: College Level MCTP Survey Instrument
Maryland Collaborative For Teaching Preparation
ATTITUDES AND BELIEFS ABOUT THE NATURE OF AND THE TEACHING
OF MATHEMATICS AND SCIENCE
COLLEGE STUDENT VERSION
Do not mark on these question sheets. Mark only on the answer sheet.
This survey is being used for research purposes only; your identity will
Thank you for your participation.
The preparation of this material was supported in part by a grant from the
National Science Foundation (Cooperative Agreement No. DUE 9255745)
MCTP Survey Instrument: Attitudes and Beliefs about the Nature of and
the Teaching of Mathematics and Science
Section One: Background Information
a. Male b. Female
a. African-American b. Asian/Pacific Islander c. Caucasian
d. Hispanic e. Other
3. Number of completed college credits:
a. 0- 30 b. 31-60 c. 61-90 d. 91+ e. post-baccalaureate
4. Major or area of concentration:
a. Education/Mathematics b. Education/Science
c. Education/Mathematics & Science d. Education/Other Subject(s)
e. Not in teacher certification program
Section Two: Attitudes and Beliefs
Below, there is a series of sentences. Indicate on your bubble sheet
the degree to which you agree or disagree with each sentence.
Your choices are:
A B C
strongly agree sort of agree not sure
sort of disagree strongly disagree
There are no right or wrong answers. The correct responses are those that
reflect your attitudes and beliefs. Do not spend too much time with any
5. I am looking forward to taking more mathematics courses.
6. I enjoy learning how to use technologies (e.g., calculators, computers,
etc.) in mathematics classrooms.
7. I like mathematics.
8. Calculators should always be available for students in mathematics classes.
9. Mathematics is a constantly expanding field
10. In grades K-9, truly understanding mathematics in schools requires special
abilities that only some people possess.
11. Before students spend much time solving mathematical problems, they
should practice computational procedures.
12. The use of technologies (e. g., calculators, computers, etc.) in mathematics
is an aid primarily for slow learners.
13. Mathematics consists of unrelated topics (e.g., algebra, arithmetic,
calculus and geometry.
14. To understand mathematics, students must solve many problems following
15. Students should have opportunities to experience manipulating materials
in the mathematics classroom before teachers introduce mathematics vocabulary.
16. Getting the correct answer to a problem in the mathematics classroom
is more important than investigating the problem in a mathematical manner.
17. Students should be given regular opportunities to think about what they
have learned in the mathematics classroom.
18. Using technologies (e.g., calculators, computers, etc.) in mathematics
lessons will improve students' understanding of mathematics.
19. The primary reason for learning mathematics is to learn skills for doing
20. Small group activity should be a regular part of the mathematics classroom.
21. I am looking forward to taking more science courses.
22 Using technologies (e.g., calculators, computers, etc.) in science lessons
will improve students' understanding of science.
23. Getting the correct answer to a problem in the science classroom is
more important than investigating the problem in a scientific manner.
24. In grades K-9, truly understanding science in the science classroom
requires special abilities that only some people possess.
25. Students should be given regular opportunities to think about what they
have learned in the science classroom.
26. Science is a constantly expanding field.
27. Theories in science are rarely replaced by other theories.
28. To understand science, students must solve many problems following examples
29. I like science.
30. I enjoy learning how to use technologies (e.g., calculators, computers,
etc.) in science.
31. The use of technologies (e. g., calculators, computers, etc.) in science
is an aid primarily for slow learners.
32. Students should have opportunities to experience manipulating materials
in the science classroom before teachers introduce scientific vocabulary.
33. Science consists of unrelated topics like biology, chemistry, geology,
34. Calculators should always be available for students in science classes.
35. The primary reason for learning science is to provide real life examples
for learning mathematics.
36. Small group activity should be a regular part of the science classroom.
ITEMS 37--46 ARE FOR ONLY THOSE INTENDING TO TEACH
37. I expect that the college mathematics courses I take will be helpful
to me in teaching mathematics in elementary or middle school.
38. I want to learn how to use technologies (e.g.,, calculators, computers,
etc.) to teach mathematics.
39. I anticipate/believe that there is very little to learn about teaching
at the elementary or middle school level by observing and reflecting on
the way the instructor in this class teaches.
40. The idea of teaching science scares me.
41. I expect that the college science courses I take will be helpful to
me in teaching mathematics and science in elementary or middle school.
42. I prefer to teach mathematics and science emphasizing connections between
the two disciplines.
43. The idea of teaching mathematics scares me.
44. I want to learn how to use technologies (e.g., calculators, computers,
etc.) to teach science.
45. I feel prepared to teach mathematics and science emphasizing connections
between the two disciplines.
46. Area of teaching certification
a. elementary (grades 1-8) b. secondary mathematics (5-12)
c. secondary science (5-12) d. other
47. I intend to teach grades
a. K - 3 b. 4-8 c. 9-12 d. post-secondary e. undecided
48. I am a student in the Maryland Collaborative for Teaching Preparation.
a. yes b. no
APPENDIX B: Faculty Interview Protocols
1. To what extent is the instruction in your class planned to highlight
connections between mathematics and science?
2. To what extent will this class involve the application of technology,
such as e-mail, CDs, computers, calculators, etc.?
3. To what extent will you make significant attempts to access your students'
prior knowledge of a topic before instruction? What techniques will you
4. To what extent do the tests and exams stress reasoning, logic, and understanding
over the memorization of facts and procedures?
5. In what ways do you think your teaching models the type of teaching that
you believe should be done in grades four through nine?
6. To what extent will you explicitly encourage your students to reflect
on changes in their ideas about topics in your class?
Reflecting over this semester's MCTP class, what new thoughts do you have
on these areas (Question 1-6):
1. Instruction planned to highlight connection among math and the science?
2. Instruction involving the application of technologies?
3. Need to access students' prior knowledge of a topic before instruction?
4. Use of assessment techniques that stress reasoning, logic and understanding
as opposed to memorization of facts and procedures?
5. Modelling the type of teaching that you believe should be done in grades
6. Need to explicitly encourage your students to reflect on changes in their
ideas in the class?
7. Reflecting back, have you seen what you have learned and experienced
with MCTP courses and experiences come through in any other professional
8. Reflecting over your course, what are the pieces unique to MCTP that
stand out in your mind that worked well or that you might change?
9. Projecting into the future, do you have plans to teach another MCTP course?
10. How do you feel about teaching another MCTP course?
11. Has your involvement with MCTP enabled you to make connections with
other MCTP faculty?
12. What kinds of things that have been part of the MCTP project have provided
support to you or have contributed to your wanting to continue in the project?
13. What constraints?